Modeling gravitational radiation from coalescing binary black holes

TL;DR

This work delivers the first astrophysical model for gravitational radiation from coalescing equal-mass, non-spinning binary black holes using the Lazarus approach, which couples far-limit, fully nonlinear, and close-limit techniques. By testing late-stage NR-CL dynamics across a sequence of initial data and connecting to an early-stage QC data model, the authors produce robust waveforms dominated by circularly polarized $l=2$, $m=\pm2$ radiation, radiating about $2.5$–$3\%$ of the total mass and about $12\%$ of the angular momentum, with a remnant spin $a/M \approx 0.7$. The study demonstrates consistency with Post-Newtonian expectations and provides practical, analytic-like plunge waveforms suitable for data analysis, while highlighting the method's resilience to reasonable variations in initial data and interface placement. The results offer a valuable bridge between numerical relativity and gravitational-wave data analysis, informing observer strategies and guiding future extensions to spinning and unequal-mass systems.

Abstract

With the goal of bringing theory, particularly numerical relativity, to bear on an astrophysical problem of critical interest to gravitational wave observers we introduce a model for coalescence radiation from binary black hole systems. We build our model using the "Lazarus approach", a technique that bridges far and close limit approaches with full numerical relativity to solve Einstein equations applied in the truly nonlinear dynamical regime. We specifically study the post-orbital radiation from a system of equal-mass non-spinning black holes, deriving waveforms which indicate strongly circularly polarized radiation of roughly 3% of the system's total energy and 12% of its total angular momentum in just a few cycles. Supporting this result we first establish the reliability of the late-time part of our model, including the numerical relativity and close-limit components, with a thorough study of waveforms from a sequence of black hole configurations varying from previously treated head-on collisions to representative target for ``ISCO'' data corresponding to the end of the inspiral period. We then complete our model with a simple treatment for the early part of the spacetime based on a standard family of initial data for binary black holes in circular orbit. A detailed analysis shows strong robustness in the results as the initial separation of the black holes is increased from 5.0 to 7.8M supporting our waveforms as a suitable basic description of the astrophysical radiation from this system. Finally, a simple fitting of the plunge waveforms is introduced as a first attempt to facilitate the task of analyzing data from gravitational wave detectors.

Figures (36)

• Figure 1:
• Figure 2: Sequence P
• Figure 3: Apparent horizons for $P_{ID}=0$
• Figure 4: S-invariant measuring deviations from Kerr
• Figure 5: Total radiated energy plots